If I take pictures of someone and hang my home with AI-generated copies of those pictures, I’m not stealing their identity.

The existence of Photoshop doesn't mean that you can put Kobe Bryant on a Wheaties box without paying him. There's no reason that a voice talent's voice can't be subject to the same infringement protections as a screen actor's or athlete's likeness.

You absolutely can put Kobe on a Wheaties box without problems legally, IF you do not sell it. That's "fair use." It has not been tested in court yet, but precedent seems to suggest that creating voice clones for private use is also fair use, ESPECIALLY if that person is a celebrity, because privacy rights are limited for celebrities.